A thin rod has length L and total mass M lies along the x axis. (a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the rod in terms of L, M, and ?̂. (b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from the left end according to the relation: ? = ? ?ଷ ?ଷ where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still M. Find λ0 and the position of the center of mass with respect to the left end of the rod. Express your answer in terms of some or all of the following: L, M, and ?̂.
A thin rod has length L and total mass M lies along the x axis. (a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the rod in terms of L, M, and ?̂. (b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from the left end according to the relation: ? = ? ?ଷ ?ଷ where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still M. Find λ0 and the position of the center of mass with respect to the left end of the rod. Express your answer in terms of some or all of the following: L, M, and ?̂.
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter10: Systems Of Particles And Conservation Of Momentum
Section10.3: Center Of Mass Revisited
Problem 10.2CE
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A thin rod has length L and total mass M lies along the x axis.
(a) Suppose the rod is uniform. Find the position of the center of mass with respect to the left end of the
rod in terms of L, M, and ?̂.
(b) Now suppose the rod is not uniform but has a linear mass density that varies with the distance x from
the left end according to the relation:
? =
?
?ଷ ?ଷ
where λ0 is a constant and has SI units of kg/m. The total mass of the rod is still
M. Find λ0 and the
position of the center of mass with respect to the left end of the rod. Express your answer in terms of
some or all of the following: L, M, and ?̂.
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